lesson parts and wholes 5 1 -...

121

Parts and Wholes LESSON

5 �1

Date Time

Work with a partner. Use counters to help you solve these problems.

1. This set has 15 counters. What fraction of the set is black?

2. If 12 counters are the whole set, what fraction of the set is 8 counters?

3. If 12 counters are the whole set, how many counters are

14 of a set?

counters

4. If 20 counters are a whole,how many counters make

45?

counters

5. If 6 counters are 12 of a set,

how big is the set?

counters

6. If 12 counters are 34 of a set,

how many counters are in the whole set?

counters

7. If 8 counters are a whole set, how manycounters are in one and one-half sets?

counters

8. If 6 counters are two-thirds of a set, how manycounters are in one and two-thirds sets?

counters

122

Finding Fractions of a WholeLESSON

5 �1

Date Time

1. In a school election, 141 fifth graders voted. One-third voted for Shira and two-thirds voted for Bree.

a. How many votes did Shira get?

b. How many votes did Bree get?

2. Bob, Liz, and Eli drove from Chicago to Denver.Bob drove 1

10 of the distance.

Liz drove 140 of the distance.

Eli drove 12 of the distance.

How many miles did each person drive?

a. Bob: miles b. Liz: miles c. Eli: miles

Check to make sure that the total is 1,050 miles.

3. Carlos and Rick paid $8.75 for a present. Carlos paid 25 of the total amount, and

Rick paid 35 of the total.

a. How much did Carlos pay?

b. How much did Rick pay?

4. A pizza costs $12.00, including tax. Scott paid 14 of the total cost. Trung paid

13 of

the total cost. Iesha paid 16. Bill paid the rest. How much did each person pay?

a. Scott: $ b. Trung: $ c. Iesha: $ d. Bill: $

5. If 60 counters are the whole, how many counters make two-thirds? counters

6. If 75 counters are 34 of a set, how many counters are in the whole set? counters

7. If 15 counters are a whole, how many counters make three-fifths? counters

141 votes

13

Shira

23

Bree

Denver

Chicago1,050 miles

CO NEIA

IL

Math Boxes LESSON

5 �1

Date Time

3. Sixty students voted for their favorite fruit. The circle graph shows the results.

a. What fraction voted for apples?

b. What fraction voted for peaches?

c. What fraction voted for strawberries?

4. Divide.

a. 843 � 28 →

b. 279 � 17 →

5. Make up a set of at least twelve numbersthat has the following landmarks. Minimum: 50 Median: 54Maximum: 57 Mode: 56

Favorite Fruits

apples18

oranges12 strawberries

15

peaches5

bananas10

123

4 23 62

59 125

11922–24

1. Write a 10-digit numeral that has7 in the billions place,5 in the hundred-thousands place,3 in the ten-millions place,4 in the tens place,8 in the hundreds place, and2 in all other places.

, , ,

Write the numeral in words.

2. Write each fraction as a whole number or a mixed number.

a. 284 �

b. 158 �

c. 261 �

d. 145 �

e. 131 �

124

Mixed Numbers: Part 1LESSON

5�2

Date Time

Fractions greater than 1 can be written in several different ways.

Example: If is worth 1, what is worth?

The mixed-number name is 2 34. (2

34 means 2 �

34.)

The fraction name is 141. (Think quarters: .)

So 2 34, 2 �

34, and

141 are just different names for

the same number.

In the problems below, the hexagon shape is worth 1.

1. �

2. �

3. �

4. �

In the problems below, the hexagon shape is worth 1.Write the mixed-number name and the fraction name shown by each diagram.

5. Mixed number = Fraction =





Rulehexagon

Rulehexagon

125

Mixed Numbers: Part 2LESSON

5�2

Date Time

For Problems 1–5, each triangle block is worth 14.

Use your , , and pattern blocks to solve these problems.

1. Cover a rhombus block with triangle blocks. A rhombus is worth .

2. Cover a trapezoid block with triangle blocks. A trapezoid is worth .

3. Arrange your blocks to make a shape worth 1. Trace the outline of each block that is part of your shape, or use your Geometry Template. Label each part with a fraction.

4. Arrange your blocks to make a shape that is worth 2 12. Trace the outline of each

block that is part of your shape, or use your Geometry Template. Label each partwith a fraction.

5. Use your blocks to cover this shape.

Trace the outline of each block and label each part with a fraction.

How much is the shape worth?

� 14

For Problems 6–10, each triangle block is worth 12.

Use your , , and pattern blocks to solve these problems.

6. What shape is worth ONE?

7. A rhombus is worth .

8. A trapezoid is worth .

9. Arrange your blocks to make a shape thatis worth 3

12. Trace the outline of each

block that is part of your shape, or use your Geometry Template. Label each part with a fraction.

10. Use your blocks to cover the shape below. Trace the outline of each block. Label each part with a fraction.

How much is the shape worth?

11. If a triangle block is 14, make a diagram to show the fraction

145.

Write 145 as a mixed number.

145 � .

126

Mixed Numbers: Part 2 continuedLESSON

5�2

Date Time

� 12

� 14

127

Fractions on a RulerLESSON

5 �2

Date Time

1. Find and mark each of these lengths on the ruler below. Write the letter above themark. Letters A and B are done for you.

A: 5" B: 12" C: 3

12" D: 2

12"

E: 4 34" F:

14" G: 4

18" H: 1

78"

I: 138" J:

1156" K: 3 1

16" L: 5 1

96"

2. a. Mark this line segment so that it is 248 inches long.

b. How many eighth-inches long is the line segment? eighth inches

c. How many quarter-inches long is it? quarter inches

d. How many half inches is it? half inches

3. Grace was supposed to mark 12 on a number line. This is what she did.

Explain Grace’s mistake.

4. Rocco said that this stick is 4136 inches long.

Explain his mistake.

AB

0 1 2 3

0 1 2 3 4 5 6inches

0 1 2 3 4 5 6inches

128

Math Boxes LESSON

5�2

Date Time

2. Use a full circle protractor to draw and label an angle MAD, whose measure is 105�.

1. Write five fractions that are equivalent to 12.

3. Raphael bought 14 pounds of meat to make hamburgers at the Fourth of July barbeque. Hecan make 5 hamburgers from each pound. Buns come in packages of 8. How manypackages of buns does Raphael need?

(unit)

Explain your answer.

4. True or false? Write T or F.

a. 5,894 is divisible by 6.

b. 6,789 is divisible by 2.

c. 367 is divisible by 3.

d. 9,024 is divisible by 4.

e. 8,379 is divisible by 9.

5. Ella reads about 48 pages in 1 hour.About how many pages will she read in

212 hours?

204–206

19 20243

11 59–61

77 78

129

Comparing and Ordering FractionsLESSON

5�3

Date Time

Math Message

Decide whether each of these measurements is closer to 0, 12, or 1 inch. Circle the

closest measurement.

1. 18 inch is closest to . . . 0 inches.

12 inch. 1 inch.


12 inch. 1 inch.


12 inch. 1 inch.


12 inch. 1 inch.

5. Explain your solution for Problem 4.

Ordering Fractions

For each problem below, write the fractions in order from least to greatest.

6. 68,

38,

58,

88 , , ,

7. 27,

29,

25, 1

22 , , ,

8. 23,

14,

13,

34 , , ,

9. 35, 140, 2

90, 2

15 , , ,

10. 37, 1

10,

78,

57 , , ,

11. 59,

25,

16, 1

90 , , ,

12. 48,

47,

35,

49 , , ,

130

Fraction-Stick ChartLESSON

5�3

Date Time

Which is larger:

47 or

45 ?

Which is larger:

47 or

38 ?

Which is larger:

1 72 or

46 ?

Which is larger:

1 23

or 43 ?

Which is closer to 1

12 :1

13 or

1 25

?

Which is

25 closest to:

0or

12 or

1?

Which is

1 36 closest to:

0or

12 or

1?

Which is

58 closest to:

0or

12 or

1?

23 �

—6

23 �

—9

23 �

—12

34 �

—8

34 �

—12 34

�—

16

21 06 �

—4

18 4�

—4

16 1�

—12

1 35

�—

51

12 �

—8

1 34

�—

16

112116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116116

116

112112

112112

112112

112112

112112

112112

112112

112112

112112

112112

112112

112

110110

110110

110110

110110

110110

110110

110110

110110

110110

110110

1919

1919

1919

1919

1919

1919

1919

1919

1919

1818

1818

1818

1818

1818

1818

1818

1818

17 1616

1616

1616

1616

1616

1616

1515

1515

1515

1515

1515

1414

1414

1414

1414

1313

1313

1313

1212

1212

11

141

2434

01

141

241

342

1717

1717

1717

1717

1717

1717

17

1.

4.

7.

10

.

2.

5.

8.

11

.

3.

6.

9.

12

.

Fill in the blanks. Circle the correct answ

er.

131

Adding with Fraction SticksLESSON

5�3

Date Time

A whole stick is worth 1.

1. Use the fraction sticks to find equivalent fractions.

a. 18 � —

16b. —

8 � 1126 � —

4c. —

8 � 34 � —

16

d. 12 � —

4 � —8 � —

16e. —

2 � 44 � —

8 � —16

2. Use the fraction sticks to add fractions with the same denominator.

Example: 18 �

28 � �

38

a. 24 �

14 � �

b. 136 � 1

96 � �

c. 116 � 1

56 � 1

86 � �

3. Use the fraction sticks to add fractions with different denominators.

a. 12 �

14 � �

b. 12 �

38 � �

c. 58 �

14 � �

d. 14 �

78 � 1

26 � �

� 1

� 8 eighths

� 16 sixteenths

� 2 halves

� 4 quarters

132

Fraction Number StoriesLESSON

5�3

Date Time

Shade the fraction sticks to help you solve these fraction number stories. Write a number model for each story.

1. Chris made pizza dough with 58 cup of white flour and

14 cup of whole wheat flour.

a. How much flour did he use in all? cup

b. Number model:

2. Sheryl’s puppy weighed 112 pounds

when it was born. After two weeks,the puppy had gained

38 pounds.

a. How much did the puppy weigh after two weeks? pounds

b. Number model:

3. Shade the fraction sticks to solve the number model. Then write a fraction numberstory that fits the number model.

a. 34 �

58 =

b. Number story:

4. Make up your own fraction number story. Draw and shade fraction sticks to solve it.Write a number model for your story.

a. Number story:

b. Number model:

c. Solution:

Math Boxes LESSON

5�3

Date Time

3. Where 32 students vacationed, ...

a. what fraction of the students traveled within their state?

b. what fraction traveled to Europe?

c. what fraction traveled to Canada or Mexico?

Canadaor Mexico

8

Europe4

anotherstate

6

stayedhome 3

within state11

Vacation Travel

1. Write a 10-digit numeral that has

9 in the tens place,3 in the millions place,5 in the billions place,7 in the hundred-millions place,1 in the thousands place, and6 in all other places.

, , ,

Write the numeral in words.

2. Write each fraction as a whole number or a mixed number.

a. 147 �

b. 234 �

c. 52 �

d. 98 �

e. 352 �

4. Divide.

a. 21�4�9�3� ∑

b. 35�6�2�3� ∑

5. Find the following landmarks for this set ofnumbers: 929, 842, 986, 978, 869, 732,898, 986, 900, 899, 986, 920, 842

a. Minimum:

b. Maximum:

c. Mode:

d. Range:

e. Median:

133

4

22–24

62 63

59 125

119

Here is a way to model equivalent fractions. Start with a fraction stickthat shows 3 out of 7 parts (

37) shaded.

Draw a horizontal line to split each part of the stick into 2 equal parts. Now 6 out of 14 parts (1

64) are shaded. So

37 � 1

64.

If each part of the original fraction stick is split into 3 equal parts, 9 out of 21 parts (2

91) are shaded. So

37 � 2

91.

1. Draw horizontal lines to split each part of each fraction stick into 2 equal parts. Then fill in the missing numbers.

a. 13 � —

6

b. 34 � —

8

c. 45 � —

10

3. Draw horizontal lines to split each part of each fraction stick into 4 equal parts. Thenfill in the missing numbers.

a. b. c.

13 � —

1234 � —12

45 �

134

Making Equivalent FractionsLESSON

5�4

Date Time

37

37 � 1

64

37 � 2

91

2. Draw horizontal lines to split each part ofeach fraction stick into 3 equal parts.Then fill in the missing numbers.

a. 13 � —

9

b. 34 � —

12

c. 45 � —12

135

Finding Equivalent FractionsLESSON

5�4

Date Time

Study the example below. Then solve Problems 1–3 in the same way. Match each fraction in theleft column with an equivalent fraction in the right column.

Then fill in the boxes on the left with either a multiplication or division symbol and a numbershowing how you changed each fraction to get an equivalent fraction.

Example: 1.�2�2

�3�3

�5�5

�2�2

37

46

318

612

36

2300

16

164

16

616

14

69

264

122

38

23

2. 3.12

1030

56

1624

1520

1415

1215

610

46

162

13

2350

1220

34

45

2380

136

Math Boxes LESSON

5�4

Date Time

4. True or False? Write T or F.

a. 1,704 is divisible by 4.

b. 7,152 is divisible by 6.

c. 8,264 is divisible by 3.

d. 4,005 is divisible by 2.

e. 2,793 is divisible by 9.

1. Write five fractions that are equivalent to 34. 2. Use a full-circle protractor to draw and

label the following angle:�TOE: 48�

3. Amanda found a can containing 237 dominoes. A full set has 28 dominoes. What is thegreatest number of complete sets that can be found in the can? Explain how you foundyour answer.

5959 204–206

22–24243 246

11 38–40219

5. Donovan runs about 2.5 miles each day.In 3 weeks, about how many miles doeshe run?

Open sentence:

Answer:

137

Math MessageLESSON

5 �5

Date Time

Mark and label 3 decimals on each number line below.

1.

2.

Writing Fractions and Decimals

Write the numbers that your teacher dictates in the first column. Use the secondcolumn to show how you change these numbers to equivalent decimals. Write thedecimal in the third column.

0.7 0.8

Fraction or Calculations Equivalent DecimalsMixed Number

9.32 9.33

Whole

large square

138

Renaming Fractions as DecimalsLESSON

5�5

Date Time

1. Fill in the missing numbers and shade the squares.Each large square is worth 1.

a. 25 �

10� 0. b.

34 �

100� 0. c.

1255 �

100� 0.

d. 230 �

100� 0. e. 5

80 �

100� 0. f. � 0.

2. Write each number below as a decimal. Then use the letters to locate the decimals on the number line.

a. 12 � . b. 1

60 � . c.

45 � . d. 1

2030 � .

e. 2225 � . f.

2510 � . g.

75 � . h. 1

1550 � .

50

Shade 25 of the square. Shade

34 of the square. Shade

1255 of the square.

Shade 230 of the square. Shade 5

80 of the square. Write as a fraction

and as a decimal.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

a

139

Rounding DecimalsLESSON

5�5

Date Time

Rounding removes extra digits from a number. Sometimes decimals are shown withmore digits than are useful. Data with too many decimal places can be misleading. Forexample, measurements with too many digits might seem more precise than theyactually are. Many calculators display results to eight or more decimal places. In mostsituations, one or two places are enough.

Example:The interest earned on a savings account at a bank is calculated to the nearest tenth ofa cent. But the bank can’t pay a fraction of a cent. Suppose one bank always roundsthe interest down, and ignores any fraction of a cent.

The First Community Bank calculates interest on one account as $17.218 (17 dollarsand 21.8 cents). The bank ignores the 0.8 (or 1

80) cent. It pays $17.21 interest.

1. Here is the calculated monthly interest on Mica’s First Community Bank savings account. Round each amount down to find the interest paid each month.

January $21.403 February $22.403

March $18.259 April $19.024

May $17.427 June $18.916

How much total interest did the bank pay Mica for these 6 months?

(Add the rounded amounts.)

Example:At the Olympic Games, each running event is timedto the nearest thousandth of a second. The timerrounds the time up to the next hundredth of asecond (not the nearest hundredth). The roundedtime becomes the official time.

11.437 seconds is rounded up to 11.44 seconds.

11.431 seconds is rounded up to 11.44 seconds.

11.430 seconds is reported as 11.43 seconds because 11.430 is equal to 11.43. Michael Johnson with his record-breaking time

140

Rounding Decimals continuedLESSON

5�5

Date Time

Example:Supermarkets often show unit prices for items. This helps customers comparisonshop. A unit price is found by dividing the price of an item (in cents, or dollars andcents) by the quantity of the item (often in ounces or pounds). When the quotient hasmore decimal places than are needed, it is rounded to the nearest tenth of a cent.

23.822 cents (per ounce) is rounded down to 23.8 cents.

24.769 cents is rounded up to 24.8 cents.

18.65 cents is halfway between 18.6 cents and 18.7 cents. It is rounded up to 18.7 cents.

3. Round these unit prices to the nearest tenth of a cent (per ounce).

a. 28.374¢ b. 19.796¢ c. 29.327¢

d. 16.916¢ e. 20.641¢ f. 25.583¢

g. 18.469¢ h. 24.944¢ i. 17.281¢

j. 23.836¢ k. 21.866¢ l. 22.814¢

4. Describe a situation involving money when the result of a computation might alwaysbe rounded up.

Electric Timer Official Time Electric Timer Official Time

10.752 s . s 20.001 s . s

11.191 s . s 43.505 s . s

10.815 s . s 49.993 s . s

21.970 s . s 1 min 55.738 s min . s

20.092 s . s 1 min 59.991 s min s

2. Find the official times for these runs. min: minute(s) s: second(s)

141

Math Boxes LESSON

5�5

Date Time

5. One week a family ate 3 12 boxes of

cereal. The next week they ate 1 34 boxes.

How many boxes did they eat in the two weeks?

6. Wilkin School 5th graders wanted todonate 5 boxes of canned food to theirlocal food bank. They collected 3

15 boxes

in 3 days. How many more boxes do they need to collect?

2. Rename each fraction as a mixed numberor a whole number.

a. 248 �

b. 366 �

c. 2152 �

d. 486 �

e. 158 �

1. Write a 4-digit number that has

3 in the hundredths place,5 in the tenths place,6 in the thousandths place, and 2 in the ones place.

.

Write this number in words.

3. Write each mixed number as an improper fraction.

a. 1 34 � b. 3

12 �

c. 2 78 � d. 4

95 �

e. 6 13 �

4. Write the following numbers in order from least to greatest.

5.03 4 74 5.3 1

35 5

25

, , , ,

28 62

71

32 668962

70

142

Writing Fractions as DecimalsLESSON

5�6

Date Time

Use a straightedge and the above chart to fill in the blanks to the right of eachfraction below. Write a decimal that is equal to, or about equal to, the givenfraction. Directions for filling in the blank to the left of each fraction will be givenin the next lesson.

13 � 0.

23 � 0.

140 � 0.

45 � 0.

18 � 0.

58 � 0.

192 � 0.

1112 � 0.

113 � 1. 1

38 � 1.

3 78 � 3. 9

56 � .

33

33

112

116

116

116

116

116

116

116

116

116

116

116

116

116

116

116

116

112

112

112

112

112

112

112

112

112

112

112

110

110

110

110

110

110

110

110

110

110

19

19

19

19

19

19

19

19

19

18

18

18

18

18

18

18

18

17

16

16

16

16

16

16

15

15

15

15

15

14

14

14

14

13

13

12

13

12

1

14 12

4340

17

17

17

17

17

17

0.0 0.1 0.2 0.3 0.50.4 0.6 0.7 0.90.8 1.0

1.

3.

5.

7.

9.

11.

2.

4.

6.

8.

10.

12.

143

Prime FactorizationLESSON

5�6

Date Time

Make a factor tree for each number. Example:Then write the prime factorization. An example has been done for you.

1. 75 2. 99

4

2 2

�

��

5

20

5

3. 56 4. 32

Write each number as the product of factors. Then find the answer.

Example: 22 � 9 � 2 � 2 � 3 � 3 � 36

5. 52 � 102 � 22 � �

6. 32 � 23 � 102 � �

7. 42 � 22 � 33 � �

Write the prime factorization for each number using exponents when possible.

Example: 36 � 22 � 32

8. 144 � 9. 1,000 � 10. 85 �

Math Boxes LESSON

5�6

Date Time

2. Estimate an answer for each problem.

a. 20.6 � 4 Estimate

b. 184.38 � 9 Estimate

c. 15.503 � 7 Estimate

d. 872.16 � 8 Estimate

4. Determine whether the following sentencesare true or false. Write T or F.

a. 3.5 � 0.35

b. 25 �

13

c. 24 � 64

d. �99� � 9

1. Complete the table.

3. Put the following decimals in order from least to greatest.

0.204

0.19

0.265

0.560

0.099

, , ,

,

144

83 8990

32 33 9 32 66

6. Circle the letters for the pairs of equivalent fractions.

a. 16,

36 b.

1255,

35

c. 23, 1

60 d.

27,

1305

e. 4586,

67 f.

49, 1

6355

5. Put the following fractions in order from least to greatest.

38,

45,

23,

14, 1

90

, , , ,

59–6166 67

42247–249

Fraction Decimal Percent

170

38

0.3—

More about Writing Fractions as DecimalsLESSON

5�7

Date Time

Sometimes when you divide without using the calculator’s fix function to limit decimalplaces, you see that the display is filled with decimal digits. If the display were bigenough, these digits would repeat forever.

Writing a bar over the digit or digits that repeat is a simple way to write theserepeating decimals. Some calculators will display repeating decimals by rounding thelast digit in the display. Study this table.

1. Explain how you would predict whether 29 or

39 is closer to 0.25 before using your calculator.

Use your calculator and convert each fraction below to a decimal by dividing thenumerator by the denominator. If the result is a repeating decimal, write a bar over thedigit or digits that repeat. Then circle the correct answer to each question.

2. Which is closer to 0.25? 29 or

39


56


172


112


176

145

Fraction Calculator Display Decimal

0.33333333333 0.3

0.66666666666 or 0.666666666667 0.6

0.08333333333 0.083

0.8888888888 or 0.8888888888889 0.8

0.045454545 or 0.045454545455 0.045

13

112

89

212

23

–

–

–

–

—

146

Math Boxes LESSON

5�7

Date Time

4. Rename each fraction as a decimal.

a. 2346 �

b. 17080 �

c. 2450 �

d. 1105 �

e. 2218 �

1. Write a 4-digit number that has

7 in the tenths place,2 in the hundredths place,0 in the ones place, and5 in the thousandths place.

.


2. Rename each mixed number as a fraction.

a. 378 �

b. 469 �

c. 10172 �

d. 823 �

e. 6154 �

3. Write each fraction as a whole number ora mixed number.

a. 159 �

b. 482 �

c. 166 �

d. 3162 �

e. 74 �

5. Nadia took three hikes. On the first hike she walked 21

40 miles. On the second

hike she walked 3110 miles, and on the third

she walked 314 miles. How far did she

walk in all?

6. Lisa is 1012 years old. In how many years

will she be 17 years old?

Open sentence:

Answer:

62 6328

62 63

70 71

83–88

Example: Teneil used her calculator to rename the following fraction as a decimal and as a percent.

Teneil needed to work with only a whole percent, so she rounded 60.86956522% to 61%.

1. Use your calculator to convert each fraction to a decimal. Write all of the digits shown inthe display. Then write the equivalent percent rounded to the nearest whole percent.The first row has been done for you.

2. Lionel got 80% of the questions correct on a spelling test. If the test had 20 questions,

how many did Lionel get correct?

3. Jamie spent 50% of his money on a baseball cap. The cap cost $15. How much

money did Jamie have at the beginning?

4. Hunter got 75% of the questions correct on a music test. If he got 15 questions correct,

how many questions were on the test?

147

Converting to Decimals and PercentsLESSON

5�8

Date Time

1243 14 23 0.6086956522 100 0.6086956522 60.86956522%



1385 0.5142857143 51%

1627

2943

1234

15,37369

5. The chart lists 6 animals and the average number of hours per day that eachspends sleeping.

Write the fraction of a day that each animal sleeps. Then calculate the equivalentdecimal and percent, rounded to the nearest whole percent. You may use yourcalculator. The first row has been done for you.

Source: The Top 10 of Everything 2005

6. The total number of horses in the world is about 60,800,000. China is the country with the greatest number of horses (about 8,900,000). What percent of the world’s horses live in China?

7. In the United States, about 45% of the population has blood type O. About how many people out of every 100 have blood type O?

8. About 11 out of every 100 households in the United States has a parakeet. How would you express this as a percent?

9. It is thought that adults need an average of 8 hours of sleep per day.

a. What percent of the day should adults sleep?

b. If infants average 16 hours of sleep per day, what percent of the day do they sleep?

148

Converting to Decimals and Percents cont.LESSON

5�8

Date Time

Average Hours Fraction of Percent ofAnimal of Sleep Day Spent Decimal Day Spent

per Day Sleeping Equivalent Sleeping

Lion and Sloth 20 2204 0.83� 83%

Opossum 19

Armadillo and 18Koala

Southern Owl 17Monkey

149

Math Boxes LESSON

5�8

Date Time

1. Complete the table.

3. Put the following decimals in order from least to greatest.

0.4, 0.14, 0.44, 0.415

, ,

,

4. Determine whether the following sentencesare true or false. Write T or F.

a. 6.05 � 2.7 � 8.75

b. If n � 4, then 3 � n � 12

c. 22 � 32 � 52

d. �64� � 8

e. 22 � �100� � 40

2. Estimate an answer for each problem.

a. 4�3�9�.0�4� Estimate

b. 8�1�7�.6� Estimate

c. 5�3�0�0�.0�0�7� Estimate

6. Circle the letters for the pairs of equivalent fractions.

a. 49,

1366

b. 1881,

29

c. 2480,

1245

d. 1105,

57

e. 255,

15

5. Put the following fractions in order from least to greatest.

37,

35,

28,

89,

56

, , , ,


23

0.95

43%

35

0.8

83 8990

42247–250

9 32 3332 33

66 67 59–61

150

Math MessageLESSON

5�9

Date Time

Tomato

es

Zucch

ini

Cucum

bers

Potatoe

s

Squas

h0

10

20

30

40

50

60

70

Bush

els

Har

vest

ed

Vegetable Crop

zucchini25%tomatoes

32%

cucumbers22%

potatoes14%

squash7%

Vegetable Crop

List how the 2 graphs above are the same and how they are different.

Similarities

Differences

Bar Graph Circle Graph

Bar Graphs and Circle (Pie) GraphsLESSON

5�9

Date Time

1. Circle the after-school snack you like best. Mark only one answer.

cookies granola bar candy bar fruit other

2. Record the class results of the survey.

cookies granola bar candy bar fruit other

Add all of the votes. Total:

The total is the number of students who voted.

3. Make and label a bar graph of the class data showing the results.

4. Another fifth-grade class with 20 students collected snack-survey data. The class made the circle graph (also called a pie graph) below.

Tell how you think they made the graph. Our Snacks

candy bar 7fruit 3

granolabar4

other 1cookies 5

151

152

Math Boxes LESSON

5 � 9

Date Time

1. Write a 4-digit number with

0 in the tenths place,4 in the thousandths place,1 in the hundredths place, and5 in the ones place.

.


2. Use the division rule to find equivalent fractions.

a. 1—8 , or 12 �

24 b. 3

96 � —12

c. 11424 � —12 d.

1449 � —2

e. 2613 � —3 , or

39 f. 1

64 � —7

3. Use the information in the bar graph to complete the circle graph.

Pizza Taco Nacho Hot Dog OtherLunch Items

Preferred Lunch

Num

ber o

f Stu

dent

s

0

20

40

60

80

100

hot d

og10

%

othe

r 5%

Title:

4. Sophie went to the ball game. She spent$8.50 on the ticket, $2.75 on a hot dog,$1.99 on a soft drink, and $0.15 on asouvenir pencil. How much did she spendin all?

5. The point totals for Team A for the last fivegames are 16, 18, 14, 12, and 15. Find thefollowing landmarks:

a. Mean:

b. Range:

c. Maximum:

d. Minimum:

66 6728

122 125

119–12134–36

153

Reading Circle GraphsLESSON

5 �10

Date Time

% %

%

%

% %

% %

% %

%

% %

% %

%

% %

%

%

%

%

%

%

%

%

%

%

For each piece of the graph, estimate what fraction and what percent of the wholecircle it represents. Label the graph pieces with the estimates. Then write yourmeasured percents in the graph legend.

1. 2.

3. 4.

154

How Much TV Do People Watch?LESSON

5 �10

Date Time

A large sample of people was asked to report how much TV they watched during oneweek. The circle graph below shows the survey’s results.

Estimate each percent. Then use your Percent Circle to measure the percent in eachcategory. Write your measures in the blanks next to the pie pieces. Two percents arefilled in for you: 18% of the people reported watching less than 7 hours, and 30%reported watching 7 to 14 hours of TV during the week.

3018

7 to 14 hours

15 to 21 hours

22 to 28 hours

Less than 7 hours

50 or more hours

43 to 49 hours

36 to 42 hours

29 to

35 ho

urs

%

%

%

%

%

%

%%

%

%

%

%

%

%

155

Measuring Angles, Perimeter, and AreaLESSON

5 �10

Date Time

1. Estimate the angle measure. Then use a protractor to measure the angle.

a. b.

Estimate: Estimate:

Measure: Measure:

2. Use a protractor to draw an angle with the given measure.

a. 75� b. 145�

3. Find the missing measurement in each figure.

a. b. c. d.

Perimeter � 42 in. Perimeter � 28 m Area � 51 m2 Area � 78 cm2

S � R � H � O �

4. The art room at Walker School is 27 feet long and 38 feet wide.

What is the area of the room?

5. Mia’s backyard is 25 feet by 50 feet. Joy’s backyard is 35 feet by 35 feet.

Who has a bigger backyard? How much bigger?

13 cm

O

17 m

H R 14 in.

S

156

Math Boxes LESSON

5 �10

Date Time

3. a. How many students prefer the class’sfavorite flavor?

b. How many more students preferchocolate to vanilla?

c. Mark your favorite flavor with an X.

4. Color the spinner so it has a 25% chanceof landing on red and a

13 chance of

landing on black. Leave the rest of thespinner white.

a. What is the probability of landing on white?

b. If you spin the spinner 300 times,about how many times would youexpect the spinner to land on black?

12

6

9 3

2

4

10

8

11

7

1

5

Num

ber o

f Stu

dent

s

0

2

4

6

8

10

12

14

Vanilla ChocolateChip

StrawberryChocolate

Fifth Grade Favorite IceCream Flavors

1. Estimate.

a. 6.32 � 3.91 ➝

b. 173.6 � 65.8 ➝

c. 3.6 � 19 ➝

d. 9.9 � 54 ➝

e. 21.6 � 100 ➝

2. Measure angle SUM to the nearest degree.

MU

S

247–250 204–206

122 125 128

157

Making Circle Graphs: Concrete RecipeLESSON

5 �11

Date Time

Concrete is an artificial stone. It is made by first mixing cement and sand with gravel orother broken stone. Then enough water is mixed in to cause the cement to set. Afterdrying (or curing), the result is a hard piece of concrete.

The cement, sand, and gravel are commonly mixed using this recipe.

Use your Percent Circle to make a circle graph for the above recipe in the circle below.Label each sector of the graph and give it a title.

Recipe for Dry Mix for ConcreteMaterial Fractional Part of Mix Percent Part of Mix

Cement 16 16

23%

Sand 13 33

13%

Gravel 12

50%

158

Making Circle Graphs: Snack SurveyLESSON

5 �11

Date Time

Your class recently made a survey of favorite snacks. As your teacher tells you the percent of votes each snack received, record the data in the table at the right. Make a circle graph of the snack-survey data in the circle below. Remember to label each piece of the graph and give it a title.

VotesSnack Number Fraction Percent

Cookies

Granola Bar

Candy Bar

Fruit

Other

Total About 100%

159

Math Boxes LESSON

5 �11

Date Time

4. Marcus had $5 to spend on lunch. Hebought a hot dog for $1.75 and someFrench fries for $0.69. How much moneydid he have left to spend on dessert?

1. Write a 5-digit number with

5 in the tens place,5 in the thousandths place, and0 in all the other places.

.


3. Use your Percent Circle and the information in the bar graph to complete the circle graph.

Title:

othe

r 5%

swimming15%Soc

cer

Swimming

Baske

tball

Bicyclin

gOthe

r

Favorite Warm Weather Sports

5th-

Gra

de S

tude

nts

0

10

20

30

40

50

5. Cheryl has a babysitting business. In fivemonths, she made the following amounts:

$28, $42, $59, $42, $64

a. Find the range.

b. Find the mode.

c. Find the median.

d. Find the mean.

2. Use the division rule to find equivalentfractions in simplest form.

a. 12050 �

b. 284 �

c. 2376 �

d. 1264 �

122 125

34–36 119–121

66 67

Sports

28

160

School DaysLESSON

5 �12

Date Time

Read the article “School” on pages 360–362 in the American Tour section of theStudent Reference Book.

1. Tell whether the statement below is true or false. Support your answer withevidence from page 360 of the American Tour.

In 1790, it was common for 11-year-olds to go to school fewer than 90 days per year.

2. About how many days will you go to school this year? About days

Write a fraction to compare the number of days you will go to school this year tothe number of days an 11-year-old might have gone to school in 1790.

3. Tell whether the statement below is true or false. Support your answer withevidence from page 361 of the American Tour.

In 1900, students in some states spent twice as many days in school, on average,as students in some other states.

4. In 1900, in which region (Northeast, South, Midwest, or West) did students go to school …

the greatest number of days per year?

the fewest number of days per year?

Try This

161

School Days continuedLESSON

5 �12

Date Time

Tell whether each statement below is true or false. Support your answer with evidencefrom the graphs on page 362 of the American Tour.

5. On average, students in 2000 were absent from school about one-third as manydays as students were absent in 1900.

6. The average number of days students spent in school per year has not changed much since 1960.

7. Tell whether the statement below is true or false. Support your answer withevidence from the American Tour.

From 1900 to 1980, the average number of days students spent in school per yearmore than doubled.

8. Locate your state in the table Average Number of Days in School per Student, 1900on page 361 of the American Tour. If you are in Alaska or Hawaii, choose another state.

Was your state above or below the median for its region?

9. Locate the number of days in school for your state in the stem-and-leaf plot on page 361 of the American Tour.

Was your state above or below the median for all states?

162

Math Boxes LESSON

5 �12

Date Time

1. Estimate. Show answers in wholenumbers.

a. 31.2 � 9.6 ➝

b. 4.82 � 47 ➝

c. 159.5 � 27.9 ➝

d. 8.13 � 2.92 ➝

e. 62.1 � 3.2 ➝

4. Color the spinner so that there is a 50%chance of landing on red and a

16 chance

of landing on black. Leave the rest of thespinner white.

What is the probability of landing on white?

If you spin the spinner 300 times, abouthow many times would you expect thespinner to land on black?

red

12

9 3

6

11

7

1

5

2

4

10

8

L D

I

FN

U

2. Measure each angle.

a. �LID measures

about .

b. �FUN measures

about .

3. Write a title and label the axes for the bargraph. Explain why you chose that title.

50 2 4 61 3 5

35

101520

3025

(title)

247–250

125 128122

204–206

163

Math Boxes LESSON

5 �13

Date Time

1. Mr. Hernandez’s class took a survey to find out when students prefer to do their homework. 125 fifth-grade students responded.

Use your Geometry Template to make a circle graph of the results. Give the graph a title. Label the sectors of the graph.

2. List a set of at least twelve numbers that has the following landmarks:

Minimum: 28 Maximum: 34 Median: 30 Mode: 29

Make a bar graph for what this set of numbers might represent.

3. If you roll a regular 6-sided die, what isthe probability of getting ...

a. 5?

b. a prime number?

c. an even number?

d. a multiple of 3?

4. Draw and label a 30� angle.

(title)

As soon as I get home 17%

After having an after-school snack 30%

Right after dinner 39%

Just before going to bed 14%

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

31

30

29

28

32

33

34

125 126

119 122

128 129 204–206

lesson parts and wholes 5 1 -...

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